But they finally got their reward for relentless second-half pressure when Spanish left-back Alonso drove in a firm, angled shot in the 73rd minute.
They should have scored a second through Abraham, but the England international’s shot was brilliantly blocked by DeAndre Yedlin.
Steve Bruce’s Magpies were preoccupied with defending for much of the match and failed to test Kepa Arrizabalaga.
The defeat means they drop into the relegation zone, although their manager will point to the fact they have now played every one of the ‘big six’ in their first nine games, bar Manchester City.
Another match and another test passed by Blues manager Frank Lampard.
With only one clean sheet in 12 games under his tenure and only five points from their tally of 14 going into the game collected at Stamford Bridge, some had begun to question whether his side could handle the pressure at home.
In the first period, the Blues looked off-colour and produced only a couple of half-chances, courtesy of Willian, while England midfielder Ross Barkley limped off injured just before the break.
But in the second half, his side looked the embodiment of the spirit of the former Blues midfielder as they persistently tested Newcastle’s defence.
After Abraham’s header came off the bar and Dubravka had pulled off a wonder-save, they finally made the breakthrough when Alonso found the keeper’s bottom left.
It was relief as much as celebration around the ground. The home side should have settled their fans’ nerves moments later but Abraham was denied by an excellent stop from Yedlin.
